Self Design: Sync Test of Non-Cohesion Bead Pile

Transcription

1 Self Design: Sync Test of Non-Cohesion Bead Pile Asaki Takahashi Physics Department, The College of Wooster, Wooster, Ohio 691, USA (Dated: Friday April 27th 218) In this research, we try to understand what is going on to the non-cohesion conical bead pile using videos and pressure sensors. We hypothesized that; whenever there is a surface activity with no edge activity, we will see some pattern of increase in the pressure sensor data, whenever there is small edge activity, we will see some pattern of decrease in the pressure sensor data, and whenever there is an edge activity along with slight surface activity, we will see some pattern of a drop decrease and then a small increase in the pressure sensor data. Watching the previously taped videos of the bead drops, we determined the type of activity for each bead drop and compared it with its corresponding pressure sensor data. We were able to pull six different bead drops that had distinct motions in the video and noticeable patterns in the data. We concluded that the evidence from these drops supports the hypothesis for all Patterns A, B, and C. We also discuss about the differences between the motion duration of what we actually see and what the pressure sensors detect. INTRODUCTION The experiment to study the phenomena of avalanches in a pile of uniform spherical beads has been studied for over two decades at The College of Wooster [1] [2]. These pieces of spherical beads act as a critical granular system when forming a conical pile. The idea of criticality is that the pile evolves into a critical state where at that point, a slight disturbance can cause either a minor or major event afterwards. To relate this concept that is also relevant to other natural patterns like earthquakes, forest fires, and the stock market. Many researchers have tackled this study from various aspects. One of the students, Gabe Dale-Gau, at The College of Wooster has created pressure sensors to attach onto the base of the pile and analyzed the data he obtained [3]. The eight pressure sensors that are placed equally on the outer side of the disk can detect how much force is applied to a certain area of the bead pile. Another student, Kyle McNickle, at The College of Wooster worked on video analysis of the avalanches of the bead pile []. With this, we have video recorded the response of the pile after every bead drop, for a short run of approximately 2 bead drops that was performed with the new pressure sensors on the base of the pile. With these two research projects that have just been finished, I will analyze the data we have of the pressures from the eight sensors using the video. I will be observing what is actually happening to the bead pile correspondence to certain unusual patterns in the pressure sensor data. For this research, I will be only focusing on the non-cohesion bead pile, and not the cohesion. hypothesis for this experiment is that when one or more of the eight lines has a decrement in the pressure vs. time graph, that means that the bead pile is experiencing some kind of avalanche at that particular side or area; some decrement. And that when there is an increment in the graph, that means that the bead pile is stabilizing within. The surface activity vs the edge activity graph in FIG. 1 shows what we generally think would happen. Surface activity shown in the y-axis is the motion that occurs on the top surface of the bead pile. The smaller the surface activity, the smaller the movement is in the center of the peak on the surface; the bigger the surface activity, the bigger the radius of the surface movement is. Edge activity is what we call when a number of beads fall off the HYPOTHESIS The pressure sensor is constantly recording data during the whole run, producing graphs with eight lines indicating the pressure each coordinate is detecting. Our FIG. 1: The hypothesis of this research shown in a Surface Activity vs. Edge Activity graph. This graph was created by Gabe Dale-Gau.

2 SyncTest_Drop8 SyncTest_Drop / 3/2 5/ 3/ /2 / / 3/2 5/ 3/ /2 / x x1 6 FIG. 2: A sample plot of pressure data from the eight sensors. The orange trace is an example of what the data would look like with a pattern of increase, possibly indicating that it is undergoing a large surface activity without any edge activity. FIG. 3: A sample plot of pressure data from the eight sensors. The orange trace is an example of what the data would look like with a pattern of decrease, possibly indicating that it is undergoing a large edge activity with minimal surface activity. edge of the pile. The smaller the edge activity, the smaller the number of beads that topple off the edge of the base; the bigger the edge activity, the bigger the avalanche and the number of beads that fall off. We predict that when there is minimal edge activity but a large surface activity, in other words motion on the surface without any beads dropping, there will a pattern of increase like shown in the top left quadrant separated by the green axis (Pattern A). In the actual data, we are looking for similar patterns like shown in the orange trace in FIG. 2. We believe this will true because the beads are adjusting on top of each other and stabilizing which creates more pressure onto the bottom beads. We also predict that when there is minimal surface activity but a large edge activity, in other words beads dropping off the sides, there will be a pattern of decrease like shown in the bottom right quadrant separated by the green axis (Pattern B). In the actual data, we are looking for similar patterns like shown in the orange trace in FIG. 3. We believe this will true because the beads are falling off which means that there is less amount of beads now forcing down onto the bottom layer of the beads, creating less pressure onto the bottom beads. This movement creates kinetic energy which initially was the force onto the beads below. We also predict that when there is a large edge activity with some surface activity, there will be a pattern of decrease followed by a slight increase like shown in the right of the top right quadrant separated by the green axis (Pattern C). In the actual data, we are looking for similar patterns like shown in the orange trace in FIG.. We believe this will true because when the beads are moving down, the energy turns into kinetic energy and when the beads stop and pack to stabilize, that kinetic energy turns back to the force onto the bottom layers SyncTest_Drop x1 6 FIG. : A sample plot of pressure data from the eight sensors. The orange trace is an example of what the data would look like with a pattern of decrease followed by increase, possibly indicating that it is undergoing a large surface activity with some edge activity. APPARATUS AND PROCEDURE First, I went through watching the videos of the bead drops. We had access to about a little over 2 bead drops for non-cohesion. I chose bead drop number 1-99 and to watch. If there was a movement after the bead had dropped, I would record the bead drop number and which coordinate(s) the motion was in. Sometimes there could be multiple coordinates, since the movement of the beads could be either in-between two coordinates or the movement was big enough to cover more than one coordinate. If there was a movement but only in the center of the pile, and not indicating that it is specifically in a certain coordinate, I would record its bead drop number and note center. If there were no movements at all after the bead hits the peak of the pile, then I would 7/ 3/2 5/ 3/ /2 /

3 3 TABLE I: bead drop number and its coordinate names for video and pressure sensor data. These are taken from a run of 1-99 and which was run on March 16th These six bead drops are ones that had unique and big enough motion in the video and had noticeable pattern in the corresponding pressure data. Bead Drop Video Data Number Coordinate Coordinate 6, , , 3, , FIG. 5: Image of the Bead pile with the name of the coordinates of where the pressure sensors are located underneath the pile of beads. skip that bead drop and not record it. As I went though the videos, I marked the bead drop number of which it had either a large surface activity and/or a large edge activity. With the bead drops that are marked, I checked within the pressure sensor data to make sure there is an usual pattern occurring at the coordinate written down for the video, or at least on the same side of the pile. Once that is verified, I went though the videos of the marked bead drops and record when the bead hits the peak of the pile, when the motion of the beads start, and when the motion of the beads end down to milliseconds. With the time of the motion of the beads start and end of the video, I calculated the total motion duration and recorded it. Now with the bead drops that are marked, I went into the pressure sensor data and found the time when an unusual pattern occurs. I recorded when the motion of the beads start and when the motion of the beads end down to milliseconds. With the time of the motion of the beads start and end of the pressure sensor data, I calculated the total motion duration and recorded it. To see the differences between the motion duration in the video and the data, I graphed a plot of motion time duration vs. bead drop. RESULT AND ANALYSIS Initially, I wanted to do this research of sync test for both cohesion and non-cohesion bead piles. When I was looking through the videos for the cohesion piles, there were no motions within the video, but rather saw the difference between the end of one video and the beginning of the preceding video. Each bead drop is at every eighty seconds but since the video camera we have takes time to save videos, we could not constantly video and save simultaneously. Therefore, the video recorded the first milliseconds (about 15.6 seconds) and took the rest of approximately 6. seconds to save the video. What must of happened with the cohesion videos is that there was an error when converting the videos and missed the actual bead drop and the motion of the bead pile movement; video recording slightly before the action happened. Because of this, I decided to only focus and study the patterns of non-cohesion piles. Because the video did not start simultaneously when the pressure sensor data started, the bead drop number in the pressure sensor data is two more than what it actually is, which is the bead drop number in the video. For example, for bead drop four, the bead drop number four in the video is the bead drop number in 6 in the pressure sensor data. Similarly, drop 5 in the video would correspond to drop 56 in the pressure sensor data. There are total of eight pressure sensors located on the outer side of the base of the bead pile as shown in FIG.5. However, not all of the eight were operating when running this non-cohesion experiment. Two sensors at 7/ and at were broken. For this, we will analyze movements of the bead pile at all but those two coordinates. When I went through the videos, there were only a few bead drops that significantly stood out. Bead drop number 6, 12, 29, 36, 162, and 167 were the bead drops that had particularly noticeable surface activity and/or edge activity, along with unique patterns in the pressure sensor data corresponding to the bead drop number. The coordinates of which the motion was in can be seen in TABLE I. The bead drop number 6 had surface activity at coordinates and / in the video as shown in FIG 6 and a unique pattern of increase at coordinate / in the pressure sensor data shown in FIG 7. The pattern we see here is similar to the shape Pattern A in FIG. 1. This corresponds to what we hypothesized. In bead drop 6,

4 FIG. 6: Screenshot taken of the bead drop number 6 video. The region within the red circle is where the motion of surface activity occurred. FIG. 8: Screenshot taken of the bead drop number 36 video. The region within the red circle is where the motion of surface activity occurred. / zy1_drop8 zy2_drop8 SyncTest_Drop8 SyncTest_Drop / zy1_drop38 zy2_drop x x1 6 FIG. 7: sensor data vs. time of bead drop number 6. The two red lines indicate the approximate average of pressure before and after the bead drop. FIG. 9: sensor data vs. time of bead drop number 36. The two red lines indicate the approximate average of we had a surface activity with motion duration about 5 ms and no edge activity. We can say that within that coordinate the beads were adjusting on top of each other creating more force between the beads giving more pressure towards the bottom of the pile. The bead drop number 12 had surface activity at coordinate 5/ in the video and a unique pattern of increase at coordinate 3/2 in the pressure sensor data. The pattern we see here is also similar to the shape Pattern A in FIG. 1. This corresponds to what we hypothesized. In bead drop 12, we had a surface activity with motion duration about 5 ms and no edge activity. Note that we may have not seen the whole duration of the motion because the movement was in coordinate 3/2, which is right under the arm of the bead dropper. Very much alike to drop 6, we can say that within that coordinate the beads were adjusting on top of each other creating more force between the beads giving more pressure towards the bottom of the pile. The bead drop number 36 had surface activity at coordinate / in the video as shown in FIG 8 and a unique pattern of increase at coordinate / in the pressure sensor data shown in FIG 9. The pattern we see here is also similar to the shape Pattern A in FIG. 1. This corresponds to what we hypothesized. In bead drop 36, we had a surface activity with motion duration about 55 ms and no edge activity. Very much alike to drop 6 and 12, we can say that within that coordinate the beads were adjusting on top of each other creating more force between the beads giving more pressure towards the bottom of the pile. The bead drop number 29 had edge activity at coor-

5 5 7 SyncTest_Drop31 SyncTest_Drop16 6 / zy1_drop31 zy2_drop / zy1_drop16 zy2_drop x x1 6 FIG. 1: sensor data vs. time of bead drop number 29. The two red lines indicate the approximate average of FIG. 11: sensor data vs. time of bead drop number 162. The two red lines indicate the approximate average of dinates / and in the video and a unique pattern of decrease at coordinate / in the pressure sensor data, shown in FIG 1. The pattern we see here is also similar to the shape Pattern B in FIG. 1. This corresponds to what we hypothesized. In bead drop 29, we had a small edge activity with motion duration about 157 ms and a little to no surface activity. We can say that within that coordinate the beads were falling off which means that there were less number of beads forcing down onto the base of the base, having less pressure onto the pressure sensors. And the pressure stays at the amount that it drops to initially. The bead drop number 162 had edge activity at coordinates 5/, 3/2, and in the video and a unique pattern of initial decrease and a slight increase at coordinate 5/ in the pressure sensor data shown in FIG 11. The pattern we see here is similar to Pattern C in FIG. 1. This corresponds to what we hypothesized. In bead drop 162, we had an edge activity of about 36 ms and little to some surface activity. We can say that within that coordinate, the beads were falling off which means that there were less number of beads forcing down onto the base of the base, having less pressure onto the pressure sensors. What makes this different from bead drop 29 is that there is a bit of increase after the big dip in the pressure sensor data. The edge activity of drop 162 was bigger than drop 29, looking at the number of bead that dropped of the edge and the motion duration, which corresponds to our hypothesis in FIG. 1. We can say that, for bigger edge activities, after all the beads had dropped when the energy was in form of kinetics, the beads leftover on the pile stabilize a bit creating a little bit of increase of pressure right after, where the kinetic energy had turned back into force. The bead drop number 167 had surface activity at coordinates and / in the video and a unique pattern of initial decrease and a slight increase at coordinate / in SyncTest_Drop / zy1_drop169 zy2_drop x1 6 FIG. 12: sensor data vs. time of bead drop number 167. The two red lines indicate the approximate average of the pressure sensor data shown in FIG 12. The pattern we see here is similar to Pattern C in FIG. 1. This corresponds to what we hypothesized. In bead drop 167, we had an edge activity of about 85 ms and little to some surface activity; a bit bigger edge activity than drop 162. Very much alike to drop 162, we can say that within that coordinate, the beads were falling off which means that there were less number of beads forcing down onto the base of the base, having less pressure onto the pressure sensors. And following this motion, the beads leftover on the pile stabilize a bit creating a little bit of increase of pressure right after. All three bead drop 6, 12, and 36, which contains surface activity in the video, showed an increase in its graph. All three bead drop 29, 162 and 167, which contains some edge activity in the video, showed a decrease in its graph. Of the three that contain edge activity, one (drop 29) with small edge activity just simply had a decrease. However two of three (drop 162 and 167), which

6 6 TABLE II: Duration of motion time measured from pressure data and video. The duration is ±15 ms since the start of motion and end of motion were visually chosen. Event Activity Bead Drop Motion duration Motion duration Number Type Number from Data (ms) from Video (ms) 1 Surface Surface Edge Surface Edge Edge Motion Duration (s) Event Number 5 6 had bigger edge activity, had a bit of increase right after the dip. With this, our hypothesis about how our graphs will look like (Pattern A, B, and C) depending on the level of surface activity and edge activity is supported by this initial analysis. There is a difficulty trying to synchronize the time of the video recorded and the pressure sensor data taken. In order for this to synchronize perfectly, we would have to be really precise when starting the run. Since I did not perform the experiment myself, and instead worked with what past students have performed previously, I don t have all of the information about when and how both of the video and data were taken. I have converted the time of the video into milliseconds with the first bead drop time as time. However, even with that there was some kind of lag between the time of video and data when looking at some motion of the bead piles. With this issue, I cannot look at when the motion start time and motion end time of the surface activity and/or edge activity, and try to synchronize that together. What I decided to do is to look at the time duration of the motion in the video and the data and see if they correspond somehow. Going through the video and the pressor sensor data, I obtained the bead drop time, start time of the motion, end time of the motion, and motion duration for all six different bead drops. What s shown in TABLE II is the motion duration of the data and the video for the six different incidents, with its activity type. FIG 13 shows the graph of TABLE II. In FIG 13, bead drop number 6 is event 1, bead drop number 12 is event 2, bead drop number 29 is event 3, bead drop number 36 is event, bead drop number 162 is event 5, and bead drop number 167 is event 6. For the bead drops with surface activity, the motion duration taken from the the pressure sensor and the motion duration taken from the video are approximately the same. For the bead drops that contained edge activity, the motion duration taken from the pressure sensor data is longer than of taken from the video. This means that when there is some kind of edge activity, in other words avalanches, the time to stabilize under the surface of the pile takes more time than the motion that we ac- FIG. 13: Duration of motion time vs bead drop of TABLE II. Bead drop number 6 is 1, bead drop number 12 is 2, bead drop number 29 is 3, bead drop number 36 is, bead drop number 162 is 5, and bead drop number 167 is 6. The red triangle represents the duration of motion time from the pressure sensor data and the blue rectangle represents the duration of motion time from the video. tually see on the surface. The edge activity of bead drop number 167 is bigger than the edge activity of bead drop number 162. We can see a pattern that the bigger the avalanche, the bigger the difference is between what the pressure sensors are detecting and what we actually see. CONCLUSION In conclusion, what we hypothesized is supported by the evidence so far. Movement of surface activity without any edge activity gives us a pattern of increase in the pressure sensor graph, movement of edge activity with a slight surface activity gives us a pattern of decrease in the pressure sensor graph, and movement of edge activity with some surface activity gives us a pattern of initial decrease, followed by a slight increase in the pressure sensor graph. We can conclude that when there is surface motion, the beads are more likely to be stabilizing within the pile creating more pressure towards the bottom of the bead pile. Alongside, we conclude that when there is small edge activity, the piles fall off the pile lessening the number of beads but also the energy turns into kinetic energy creating less pressure onto the sensors. Finally, we can conclude that when there is a bigger edge activity, after many beads fall off which lessens the force onto the base, they stabilize a bit creating a bit more pressure. We can see a pattern in the difference between the motion duration of what is actually seen and of what the pressure sensors are receiving depending on if they are going through a surface activity or a edge activity. For surface activity, same amount of time is measured in data and video. For edge activity, amount of time taken from the pressure data is larger than what s actu-

7 7 ally being seen. I concluded that this means that for big avalanches, the beads are still adjusting under the top surface of the pile, even though we can t visually see the motion anymore. There are a few improvements we can make for further research. Since this study was only focused on the noncohesion runs, we can definitely try to analyze and sync the cohesion runs and see if there are any differences in the conclusion. Another thing is that this is the first time ever to sync the video and data to try to understand the meaning behind the data. Therefore I only had limited amount of bead drops to analyze; additionally, not many big avalanches. We can definitely look at more avalanches and large surface activity to prove what I have concluded in this paper to be true. By observing more bead drops, we can also tackle the rest of the three patterns that we have hypothesized in FIG. 1. The last thing that could be improved is trying to synchronize the video and the data when starting the experiment initially. This will help us understand what certain patterns present certain motions on the pile down to the seconds or even milliseconds. the appropriate direction. I would also like to thank Kyle McNickle for taking his time to convert the videos into the right format and allowing me to use them, and Gabe Dale-Gau for taking his time to assist me with operating Igor and allowing me to use his data. [1] Costello, Rachel M., et al., Self-Organized Criticality in a Bead Pile. Physical Review E. Vol 67. (25 April 23). [2] Lehman, S.Y., Baker, E., Henry, H.A., Kindschuh, A.J., Markley, L.C., Browning, M.B., Mills, M.E., Winters, R.M., and Jacobs, D.T, Avalanches on a conical bead pile: scaling with tuning parameters. Granular Matter. Vol 1. pp (212). [3] Dale-Gau, Gabe Employing a System of Sensors to Characterize Avalanche Dynamics over a Conical Bead Pile. Senior Independent Study, The College of Wooster. (22 March 218). [] McNickle, Kyle A Visual Investigation of Criticality: Avalanche Classification on a Conical Bead Pile. Senior Independent Study, The College of Wooster. (26 March 218). ACKNOWLEDGEMENTS I would like to thank Professor Lehman for guiding me through to help me better understand and advise me to